Question: $(8-i)-(-82+2i)=$ Express your answer in the form $(a+bi)$.
Background Complex numbers can be added or subtracted by separately adding or subtracting their real and imaginary terms. To add or subtract complex numbers: Expand parentheses (attending to minus signs outside of parentheses if necessary) Combine all real terms (terms that do not contain $i$ ), and add or subtract them. Combine all imaginary terms (terms that contain $i$ ), and add or subtract them. Combining Like Terms $\begin{aligned} ({8}{-}i)-({-82}+{2}i)&={8}{-}i+{82}-{2}i \\\\ &={8}+{82}{-}i-{2}i \\\\ &={90}{-3}i \end{aligned}$ Summary $({8}{-}i)-({-82}+{2}i)={90}{-3}i$